1. **State the problem:** Fully factorise the quadratic expression $x^2 - 20x - 44$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multiply to $ac$ and add to $b$. 3. **Identify coefficients:** Here, $a=1$, $b=-20$, and $c=-44$. 4. **Calculate product $ac$:** $1 \times (-44) = -44$. 5. **Find two numbers that multiply to $-44$ and add to $-20$:** These numbers are $-22$ and $2$ because $-22 \times 2 = -44$ and $-22 + 2 = -20$. 6. **Rewrite the middle term using these numbers:** $$x^2 - 22x + 2x - 44$$ 7. **Group terms:** $$(x^2 - 22x) + (2x - 44)$$ 8. **Factor each group:** $$x(x - 22) + 2(x - 22)$$ 9. **Factor out the common binomial:** $$(x + 2)(x - 22)$$ **Final answer:** The fully factorised form is $$(x + 2)(x - 22)$$.